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A uniform disc of mass m and radius R is pivoted at its centre O with its plane vertical as shown in diagram, A circular portion of disc of radius R 2 is removed from it. The time period of small oscillations of the remaining portion about O is

Options

  1. A3 π R g
  2. Bπ 1 3 R g
  3. C2 π 3 9 R 1 6 g
  4. D2 π 7 R 6 g

Correct answer

B. π 1 3 R g

Step-by-step solution

I = MR 2 2 - 1 2 M 4 R 2 2 + M 4 R 2 2 = 1 3  MR 2 3 2 and y cm = R 6 and m = 3 M 4 Time period of a physical pendulum is, T = 2 π I mgy cm ⇒ T = 2 π 1 3 4 R g

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